2022/03/16 by Rose Kaplan-Kelly, Kaplan-Kelly, Rose · 1 citation
Computer Science · Engineering · Mathematics · #57M50 #Adhesion, Friction, and Surface Interactions #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2203.08963
openalex publication_date 2022/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Traditionally, alternating links are studied with alternating diagrams on S2 in S3. In this paper, we consider links which are alternating on higher genus surfaces Sg in Sg × I. We define what it means for such a link to be right-angled generalized completely realizable (RGCR) and show that this property is equivalent to the link having two totally geodesic checkerboard surfaces, equivalent to each checkerboard surface consisting of one type of polygon, and equivalent to a set of restrictions on the link's alternating projection diagram. We then use these diagram restrictions to classify RGCR links according to the polygons in their checkerboard surfaces, provide a bound on the number of RGCR links for a given surface of genus g, and find an RGCR knot. Along the way, we answer a question posed by Champanerkar, Kofman, and Purcell about links with alternating projections on the torus.